In this article, we select corresponding Tersoff potential energy to build potential energy model and investigate the thermal conductivities of single-crystal carbon thin-film. The equilibrium molecular dynamics (EMD) method is used to calculate the nanometer thin film thermal conductivity of diamond crystal at crystal direction (001), and the non-equilibrium molecular dynamics (NEMD) is used to calculate the nanometer thin film thermal conductivity of diamond crystal at crystal direction (111). The results of calculations demonstrate that the nanometer thin film thermal conductivity of diamond crystal is remarkably lower than the corresponding bulk experimental data and increase with increasing the film thickness, and the nanometer thin film thermal conductivity of diamond crystal relates to film thickness linearly in the simulative range. The nanometer thin film thermal conductivity also demonstrates certain regularity with the change of temperature. This work shows that molecular dynamics, applied under the correct conditions, is a viable tool for calculating the thermal conductivity of nanometer thin films.